Forests are a major component of the global carbon cycle, and accurate estimation of forest carbon stocks and fluxes is important in the context of anthropogenic global change. Airborne laser scanning (ALS) data sets are increasingly recognized as outstanding data sources for high-fidelity mapping of carbon stocks at regional scales. We develop a tree-centric approach to carbon mapping, based on identifying individual tree crowns (ITCs) and species from airborne remote sensing data, from which individual tree carbon stocks are calculated. We identify ITCs from the laser scanning point cloud using a region-growing algorithm and identifying species from airborne hyperspectral data by machine learning. For each detected tree, we predict stem diameter from its height and crown-width estimate. From that point on, we use well-established approaches developed for field-based inventories: above-ground biomasses of trees are estimated using published allometries and summed within plots to estimate carbon density. We show this approach is highly reliable: tests in the Italian Alps demonstrated a close relationship between field- and ALS-based estimates of carbon stocks (r2 = 0·98). Small trees are invisible from the air, and a correction factor is required to accommodate this effect. An advantage of the tree-centric approach over existing area-based methods is that it can produce maps at any scale and is fundamentally based on field-based inventory methods, making it intuitive and transparent. Airborne laser scanning, hyperspectral sensing and computational power are all advancing rapidly, making it increasingly feasible to use ITC approaches for effective mapping of forest carbon density also inside wider carbon mapping programs like REDD++.